1 Rapid bedrock uplift in the explained by viscoelastic response to

2 recent ice unloading

3

4 Grace A. Nielda*, Valentina R. Barlettab, Andrea Bordonic, Matt A. Kingd,a, Pippa L.

5 Whitehousee, Peter J. Clarkea, Eugene Domackf, Ted A. Scambosg, Etienne Berthierh

6

7 aSchool of Civil Engineering and Geosciences, Newcastle University, Newcastle upon Tyne,

8 UK.

9 bDTU Space, Technical University of Denmark, Lyngby, Denmark.

10 cDTU Physics, Technical University of Denmark, Lyngby, Denmark; DTU Compute,

11 Technical University of Denmark, Lyngby, Denmark.

12 dSchool of Land and Food, University of Tasmania, Hobart, Australia.

13 eDepartment of Geography, Durham University, Durham, UK.

14 fDepartment of Geoscience, Hamilton College, 198 College Hill Road, Clinton New York,

15 USA 13323; now at: College of Marine Science, University of South Florida, St. Petersburg,

16 Florida, USA.

17 gNational Snow and Ice Data Center, CIRES, University of Colorado, Boulder, Colorado,

18 USA.

19 hCentre National de la Recherche Scientifique, LEGOS, Université de Toulouse, Toulouse,

20 France.

21 *Corresponding author. E-mail address: [email protected]. Tel.:+44 (0)191 222

22 6323.

23

1

24

25 Abstract

26 Since 1995 several ice shelves in the Northern Antarctic Peninsula have collapsed and

27 triggered ice-mass unloading, invoking a solid Earth response that has been recorded at

28 continuous GPS (cGPS) stations. A previous attempt to model the observation of rapid uplift

29 following the 2002 breakup of Larsen B Ice Shelf was limited by incomplete knowledge of

30 the pattern of ice unloading and possibly the assumption of an elastic-only mechanism. We

31 make use of a new high resolution dataset of ice elevation change that captures ice-mass loss

32 north of 66°S to first show that non-linear uplift of the Palmer cGPS station since 2002

33 cannot be explained by elastic deformation alone. We apply a viscoelastic model with linear

34 Maxwell rheology to predict uplift since 1995 and test the fit to the Palmer cGPS time series,

35 finding a well constrained upper mantle viscosity but less sensitivity to lithospheric thickness.

36 We further constrain the best fitting Earth model by including six cGPS stations deployed

37 after 2009 (the LARISSA network), with vertical velocities in the range 1.7 to 14.9 mm/yr.

38 This results in a best fitting Earth model with lithospheric thickness of 100–140 km and

39 upper mantle viscosity of 6 × 1017 – 2 × 1018 Pa s - much lower than previously suggested for

40 this region. Combining the LARISSA time series with the Palmer cGPS time series offers a

41 rare opportunity to study the time-evolution of the low-viscosity solid Earth response to a

42 well-captured ice unloading event.

43

44 Key Words: Antarctic Peninsula, Larsen B, ice-mass loss, viscoelastic uplift, GPS, upper

45 mantle viscosity.

46

47

2

48 1. Introduction

49 Rapid changes in climate in the Antarctic Peninsula (AP) over the past 50 years have led

50 to the retreat and eventual collapse of several major ice shelves (Fig. 1), such as Prince

51 Gustav and Larsen A in 1995 (Rott et al., 1996), and Larsen B in 2002 (Rack and Rott 2004)

52 (see Cook and Vaughan (2010) for a complete summary). In response to ice shelf collapse,

53 tributary glaciers have exhibited acceleration and thinning (e.g., De Angelis and Skvarca

54 2003; Rignot et al., 2004; Scambos et al., 2004) and this dynamic ice loss induces a solid

55 Earth response which may be observed in GPS records.

56 The study of Thomas et al. (2011) identified markedly-increased uplift in GPS coordinate

57 time series from the Northern Antarctic Peninsula (NAP) that they associated with ice

58 unloading related to the breakup of Larsen B Ice Shelf in 2002. This uplift was best captured

59 in the near-continuous cGPS record at Palmer station which exhibited an increase in uplift

60 rate from 0.1 mm/yr prior to 2002.2, to 8.8 mm/yr thereafter. Thomas et al. (2011) suggested

61 that the effect was due to the elastic response of the solid Earth but they were not able to

62 satisfactorily reproduce the increased uplift rates with an elastic model, which they suggested

63 was at least partly due to the weakly defined magnitude and spatial pattern of ice-mass loss in

64 their model.

65 The NAP lies in a complex tectonic setting which passes from active subduction along the

66 South Shetland Trench, located north of the South Shetland Islands, to passive margin west of

67 65°W at the intersection of the Hero Fracture Zone with the Shetland Platform (see Fig. S1 in

68 the supplementary material). The Bransfield Basin separates the South Shetland Islands from

69 the NAP and has active volcanism along a mid-axial region, suggesting a back arc tectonic

70 setting (Barker and Austin 1998; Barker et al., 1991). The conversion from active subduction

71 to passive margin, and hence mantle conditions more likely reflective of low viscosity, took

72 place relatively recently at ~4 Ma before present along the AP margin just south of Hero

3

73 Fracture Zone (Barker et al., 1991). One of the GPS stations used in this study (ROBI, see

74 Section 2.1) lies along a presumed incipient rift axis as expressed by the active volcanic chain

75 of the Seal Nunataks (González-Ferrán 1983). However, there is little known in relation to

76 the mantle or crustal configuration beneath the Seal Nunatak region. The reader is referred to

77 Barker (1982) and Larter and Barker (1991) for a full tectonic history of the region. Due to

78 the active tectonic setting of the region, the mantle is likely to have a relatively low viscosity

79 compared with other locations undergoing deformation in response to changes in ice-mass

80 e.g. East or Fennoscandia. Using a combination of inferred ice history, GPS and

81 GRACE data, Ivins et al. (2011) suggested this region has a relatively thin lithosphere (20-

82 45 km) and a low viscosity mantle (3-10 × 1019 Pa s). Due to the low viscosity nature of the

83 upper mantle, the Earth’s viscous response to ice-mass change in the AP is much more rapid

84 than in other regions of Antarctica, and post-1995 unloading events may hence be

85 contributing to the observed uplift in the NAP through viscoelastic rebound. Likewise,

86 assuming a Maxwell rheology, there may be very little, to no, residual response of the NAP

87 to unloading events associated with recession from the Last Glacial Maximum.

88 In this study we use cGPS data from the NAP to constrain a local model of solid Earth

89 response to a high resolution present-day mass loss field (Scambos et al., 2014, in review).

90 By comparing the modelled elastic uplift time series with the observed cGPS uplift time

91 series from Palmer Station we show that elastic uplift alone cannot reproduce the cGPS

92 observations. A viscoelastic model is then used to predict uplift based on a range of Earth

93 models, and results are compared with the Palmer record to obtain the range of best fitting

94 models. Finally, the Earth model is further refined using six shorter cGPS time series from

95 the NAP (see Table 1).

96

97 2. Data

4

98 2.1. GPS

99 Fig. 1 shows the locations of available cGPS sites in the NAP. Of these, we used the

100 seven sites closest to the region of ice-mass change (see Table 1). Palmer is a long term

101 station with an excess of 15 years of data, and the remaining six sites were installed in 2009-

102 2010 as part of the LARISSA project (LARsen Ice Shelf System, Antarctica)

103 (http://www.hamilton.edu/expeditions/larissa). We did not use the record from O’Higgins (a

104 compilation of three records from two adjacent stations, OHIG, OHI2, OHI3; labelled OHI2

105 on Fig. 1) as a constraint as it lies far from the region of largest mass loss and as such may be

106 affected by potential lateral heterogeneity in Earth structure. Spring Point (Bevis et al., 2009)

107 (SPPT on Fig. 1) was also excluded due to the lack of data at this site; however we compare

108 our results with both of these records in the supplementary material.

109 The cGPS data from 1998 through to the end of 2012 were processed using a Precise

110 Point Positioning strategy (Zumberge et al., 1997) within GIPSY-OASIS v6.1.2.

111 Homogeneously reprocessed (as of 2012) satellite clocks and fiducial-free orbits were fixed

112 to values provided by the Jet Propulsion Laboratory. The receiver clocks, tropospheric zenith

113 wet delay, tropospheric gradients and station coordinates were estimated in standard ways

114 (e.g. Thomas et al., 2011). For the troposphere, we adopted the Vienna Mapping Function v1

115 (Boehm et al., 2006) and we assumed hydrostatic zenith delays based on the European Centre

116 for Medium-Range Weather Forecasts. Higher order ionospheric effects (Petrie et al., 2011)

117 were not corrected. Solid Earth tides were corrected according to the IERS 2010 conventions

118 (Petit and Luzum 2010) and ocean tide loading displacements were corrected based on the

119 TPXO7.2 ocean tide model (Egbert et al., 2009), which has been shown to perform very well

120 in this region (King et al., 2011), using the SPOTL software (Agnew 1996; Agnew 1997) in a

121 centre of mass of the whole Earth system (CM) reference frame (Fu et al., 2012). We fixed

122 carrier phase ambiguities to integers where possible (Bertiger et al., 2010). Observations were

5

123 weighted according to their elevation-dependent scatter from a preliminary, but otherwise

124 identical, solution.

125 Fiducial-free daily site coordinates were transformed into the ITRF2008 (Altamimi et al.,

126 2011) using a 6-parameter transformation and then corrected for changes in atmospheric

127 pressure loading using global 2.5 × 2.5 degree grids of loading, in a centre of figure of the

128 Earth (CF) reference frame, derived from the National Center for Environmental Protection

129 (NCEP) reanalysis surface pressure dataset (van Dam 2010). The correction was applied by

130 removing a daily average displacement with respect to a mean reference value. Large outliers

131 from the DUPT time series were manually identified and removed, and then a median filter

132 was applied to all time series. We only consider the height time series in this paper.

133 Velocities and realistic uncertainties were estimated using the CATS software (Williams

134 2008), along with annual and semi-annual harmonics. cGPS time series contain time-

135 correlated noise which inflates the true velocity uncertainties relative to the formal errors

136 obtained from a conventional linear regression. We consider a, now common, white noise

137 plus flicker noise model using the CATS software from which we determine velocity

138 uncertainties. We scale these to 2-sigma for subsequent use. Velocities and 2-sigma

139 uncertainties for each cGPS site are given in Table 1. Below we compare model output both

140 to the height time series and to vertical velocities derived from the time series. For

141 consistency, all model-predicted uplift rates were estimated over the same time period as the

142 cGPS observed uplift rate.

143 2.2. Ice-Mass Loss

144 The input ice load model is based on a dataset of elevation change derived from Digital

145 Elevation Model (DEM) differencing and ICESat data covering the NAP region north of

146 66°S. The time span of the data varies for different sub-regions. For the Larsen B tributary

147 glaciers data are available for two time periods, 2001-2006 (Shuman et al., 2011) and 2006-

6

148 2011 (Berthier et al., 2012). Comparing the two time-periods reveals differences in spatial

149 patterns of elevation change (Figs. 1b,c) but the overall estimated mass loss during these two

150 periods differs by less than 10% (Berthier et al., 2012). For the areas north and west of Larsen

151 B, the data span the period 2003-2009 (Scambos et al., 2014, in review). In all cases we take

152 the rate of ice-mass change as being constant throughout the respective data periods; we

153 discuss extrapolations to other time periods later.

154 The data were converted to a set of 17846 loading discs with areas between 0.9 and

155 1.1 km2 for input to the model, where the height of each disc represents a mass loss or gain,

156 using an ice density of 900 kg/m3 to convert to equivalent water height following Berthier et

157 al. (2012). Data gaps over large glaciers were infilled using an inverse distance weighting

158 algorithm (inpaint_nans within Matlab). Discs with very small mass change in the range

159 ±0.5 mweq/yr have a negligible effect on deformation at sites tens to hundreds of km distance

160 from the source of loading and were discounted from the ice load model to speed

161 computation time. This was tested using the best fitting Earth model and resulted in no more

162 than ±0.2 mm/yr differences in uplift rates at the cGPS sites. The resulting ice-mass change

163 model is shown in Fig. 1a with the two periods of mass change for Larsen B glaciers, 2001-

164 2006 and 2006-2011, shown separately in Figs. 1b and 1c, respectively. The uncertainty on

165 the elevation change dataset is ±1 m/yr (2-sigma) (Scambos et al., 2014, in review), and this

166 error bound was used to create upper and lower limits on our input ice load model.

167 The pattern of mass loss for glaciers feeding the former Prince Gustav and Larsen A ice

168 shelves prior to 2001 is not known. However, there is evidence that these glaciers reached

169 their current velocities within a few years of the breakup in 1995 (Rott et al., 2008), and this

170 velocity has been maintained 15 years after ice shelf collapse (Rott et al., 2011). Observations

171 of the glaciers feeding the more southern former Wordie Ice Shelf (Wendt et al., 2010),

172 which disintegrated in a series of events between 1966 and 1989, also suggest that high rates

7

173 of mass loss are sustained over decades. We therefore assume that the observed mass changes

174 for these northerly regions are representative of ice-mass loss from 1995 to the present-day.

175 We do not model any ice history before 1995, but instead take account of any ongoing

176 deformation related to ice-mass changes before this time by estimating a linear background

177 rate from the Palmer cGPS observations (see Section 3.1). In detail, we assumed that mass

178 loss in a region began at the half year mark after the collapse of the corresponding ice shelf

179 (i.e. 1995.5 for Prince Gustav and Larsen A glaciers, and 2002.5 for Larsen B glaciers), and

180 continued at the same rate to present-day (2013.0). For the Larsen B glaciers this is clearly

181 justified, as Scambos et al. (2004) show glacier acceleration and thinning commenced a few

182 months after ice shelf collapse. We assumed that the Larsen B tributary glaciers were not

183 losing significant mass before 2002.5 and set these discs to zero change between 1995.5 and

184 2002.5 accordingly. Any elevation changes that occurred away from former ice shelf regions

185 were assumed to be part of a multi-decadal trend and associated mass changes were applied

186 for the full modelling period. These were generally small and have little effect on our

187 modelling. Although widespread glacier retreat is seen on the western Peninsula (Cook et al.,

188 2005; Pritchard and Vaughan 2007), thinning appears to be generally limited to a small

189 section at the front of the glaciers and, importantly for this study, the pattern is changing

190 relatively slowly with time (Kunz et al., 2012). Because the Larsen A and Prince Gustav

191 glaciers are distant from our cGPS sites (150-300 km from Palmer), and the uplift signals due

192 to mass changes in these areas and on the western Peninsula are linear, errors in the above

193 mentioned assumptions have only a small effect on the conclusions drawn from our

194 modelling based on the non-linearity in the Palmer record.

195

196 3. Modelling

197 3.1. Elastic Modelling

8

198 The elastic uplift was computed with the elastic component of the software VE-HresV2

199 output (Visco-Elastic High Resolution technique for Earth deformations) (Barletta et al.,

200 2006) (Barletta et al., manuscript in preparation), which is based on a compressible,

201 spherically symmetric, self-gravitating Earth. Green’s functions were spatially convolved

202 with the ice loading discs according to the methods presented in Barletta et al. (2006). Load

203 Love numbers, based on the PREM Earth structure (Dziewonski and Anderson 1981), were

204 computed in the centre of mass reference frame up to a maximum spherical harmonic degree

205 of 3700 using VE-CL0V3RS v1.4 (Visco-Elastic Compressible LOVe numbER Solver)

206 (Barletta et al., in prep.) and the degree-1 Love number was computed as described by Spada

207 et al. (2011). By using the assumption that the elastic Love numbers become asymptotic after

208 the maximum degree, the software implementing the High Resolution technique allows us to

209 capture the loading concentrated on glaciers a few km wide (Barletta et al., 2006). In this

210 way, the resolution is limited only by the resolution of the input loading discs.

211 A time series of modelled elastic uplift was computed at the location of Palmer and

212 compared with the cGPS observations (Fig. 2). As the cGPS observations are recorded

213 relative to an arbitrary reference height and the model output is relative to zero uplift at the

214 start of the modelled time period, the cGPS observations have been offset to correct for this

215 based on their pre-2002 mean. To account for the effects of centennial- or millennial-scale

216 glacial isostatic adjustment (GIA) in the cGPS record we also estimated a ‘background’

217 vertical rate by subtracting the modelled elastic uplift rate from the cGPS uplift rate over the

218 linear part of the Palmer record (1998-2002). This gives the uplift rate due to any ice-mass

219 changes prior to the start of our ice loading model, assuming an elastic-only response to post-

220 1995 events. This rate was then included in our model-predicted time series so that model

221 output could be directly compared with cGPS observations.

222 3.2. Viscoelastic Modelling

9

223 The viscous uplift of the Earth in response to the ice-mass loss was computed using the

224 compressible viscous component of the software VE-HresV2 output, which uses VE-

225 CL0V3RS v1.4 to compute the elementary viscoelastic time-dependent Green’s functions

226 (convolved with Heaviside function) up to degree 1195, and assumes that at higher degrees

227 they do not change with time so the combined Green's function is negligible. This was

228 verified when choosing the maximum degree so that the results do not suffer from effects of

229 truncation and, as for the elastic modelling, we were able to capture the response from

230 glaciers a few km wide. We limit our study to a Maxwell rheological model. It is worth

231 noting that models with alternative and more complex rheologies may also sufficiently

232 explain the observations, however at present the dataset is too sparse to resolve or require

233 them; we return to this point in the discussion.

234 We adopt a four-layer viscosity structure consisting of an elastic lithosphere, and a

235 viscoelastic upper mantle, transition zone and lower mantle, as shown in Table 2. The density

236 structure of the model consists of 31 finer layers with densities from the PREM Earth

237 structure (Dziewonski and Anderson 1981). We define a simple four-layer viscosity model as

238 the limited data do not allow a more complex model to be resolved. This is discussed further

239 in Section 5.

240 We searched for the range of plausible best-fit Earth models by varying the lithospheric

241 thickness between 20 km and 160 km, and the upper mantle viscosity between 1 × 1017 and

242 1 × 1020 Pa s. Given that Simms et al. (2012) suggest a value of 1-2 × 1018 Pa s for the South

243 Shetland Islands, which lie closer to the active subduction zone than our study region, and

244 typical values of mantle viscosity proposed for Patagonia, Iceland, or Alaska are in the range

245 1 – 10 × 1018 Pa s (Auriac et al., 2013; Lange et al., 2014; Sato et al., 2011), mantle

246 viscosities below 1 × 1017 Pa s are not thought to be physically realistic for this region of the

247 Earth. All other parameters remained fixed. Below the upper mantle layer is a transition zone

10

248 between 400 and 670 km depth with a fixed viscosity of 4 × 1020 Pa s, as suggested by Sato et

249 al. (2011) in their study of the Earth’s response to ice-mass change in Alaska; and below this,

250 a lower mantle with a fixed viscosity of 1 × 1022 Pa s. Sensitivity to different mantle layer

251 thicknesses and a more complex Earth structure will be discussed later in Section 5.

252 3.3. cGPS Constraints

253 The uplift time series output from the viscous model were added to the modelled elastic

254 uplift and the background rate, which was recalculated as described in Section 3.1, this time

255 by subtracting the modelled viscoelastic uplift rate from the cGPS uplift rate between 1998

256 and 2002. The resulting uplift time series for each Earth model in the parameter space was

257 then compared, first of all, with the Palmer cGPS observations only. In order to determine the

258 range of Earth models consistent with our data, the RMS misfit between the modelled uplift

259 and the cGPS uplift was calculated and is shown in Fig. 3a.

260 In an attempt to place further constraints on the range of well-fitting Earth models, we

261 repeated the viscoelastic modelling to calculate uplift at the six LARISSA cGPS locations

262 (Fig. 1) for the full range of Earth models. By assuming that any lateral changes in Earth

263 structure are minimal over the distance spanned by the cGPS stations (a maximum of

264 300 km), all sites can be used as constraints on a 1-D Earth model. The RMS misfit was

265 computed again by comparing the model-predicted uplift (viscoelastic + background) with

266 the cGPS observed uplift at all seven stations. When computing the modelled time series at

267 the LARISSA stations, which were not occupied prior to the Larsen B break-up, we assumed

268 that the background rate previously calculated for Palmer was representative of the whole

269 region. That is, we assumed a spatially constant background rate across all seven cGPS sites;

270 this is supported by the closeness of fit of the initial Palmer-constrained model to most of the

271 LARISSA sites (residual uplift rates in Table 3). Our assumption implies that the sites would

272 have been uplifting at lower rates prior to 2002 and the time series would be non-linear,

11

273 similar to that observed at Palmer. The implications of assuming a spatially-constant

274 background rate are discussed later in Section 5.1. At present, we do not attempt to include

275 geologic constraints on the background uplift rate, such as from marine limits and deglacial

276 chronologies, as most sites (but not all) lack evidence suitable for long-term estimates of

277 glacial isostatic adjustment.

278

279 4. Results

280 4.1. Elastic Modelling

281 The Palmer cGPS record displays significant non-linearity after 2002; however, the

282 results of the elastic modelling show that even within the uncertainty bounds of the ice-mass

283 change data (±1 m/yr), these changes in rate cannot be explained by elastic uplift only. In

284 fact, more than five times the amount of observed mass loss (i.e. five times the mass loss

285 shown in Fig. 1, applied to each disc) would be required to reproduce the magnitude of the

286 observed uplift (modelled uplift shown by the green line in Fig. 2). This is not plausible and

287 so we reject the possibility of missing ice unloading in our model, as the missing mass would

288 not only need to be large, or be very close to Palmer, but also sustained from 2002 to present.

289 Such a large signal would require a major ice shelf collapse or substantial glacier mass-loss

290 adjacent to Palmer and neither scenario exists. Consequently, we conclude that less than half

291 of the rapid increase in uplift at Palmer can be accounted for by elastic rebound, and examine

292 if additional viscous uplift may help explain the remaining cGPS uplift signal.

293 4.2. Viscoelastic Modelling Constrained by PALM

294 The RMS misfit between the modelled uplift and the Palmer cGPS uplift is shown in Fig.

295 3a. The best fitting Earth models, lying within the 95% confidence limit of observational

296 residuals, have a lithospheric thickness in the range 20-160 km and an upper mantle viscosity

297 in the range 1 × 1017 - 2 × 1018 Pa s. There is some trade-off between the two parameters,

12

298 with thicker lithosphere models accompanying a lower viscosity mantle and vice versa. The

299 Earth model with the lowest RMS misfit (4.67 mm) has values of 130 km and 7 × 1017 Pa s.

300 Computing the RMS again with a shortened time series ending in 2011 to coincide with the

301 ice-mass change data, results in a best fitting model with a lithospheric thickness of 20 km.

302 There is a possible offset in the Palmer time series during 1999 and only using data after this

303 time (and recomputing the background rate appropriately) results in a best fitting model with

304 a lithospheric thickness of 30 km. This highlights that the lithospheric thickness is poorly

305 constrained within our model, although the upper mantle viscosity is robustly found to be less

306 than 2 × 1018 Pa s in all cases.

307 For the Earth model with lowest RMS misfit to the Palmer time series, we compared the

308 model-predicted velocities at all cGPS sites with observed velocities (Table 3). The model

309 over-predicts uplift at CAPF by 2.8 mm/yr (compared with a 2-sigma uncertainty of

310 2.9 mm/yr) and under-predicts uplift at DUPT by 2.4 mm/yr, which is the only significant

311 residual, but the misfit here is only ~23% of the modelled uplift. The model performs well at

312 the other four LARISSA sites with misfits in uplift rate <2 mm/yr and within the 2-sigma

313 observational error.

314 4.3. Viscoelastic Modelling Constrained with all cGPS Records

315 Constraining the Earth model using uplift data from only one cGPS location results in an

316 upper mantle viscosity that is relatively well constrained, but with a broad range of

317 acceptable values of lithospheric thickness. Fig. 3b shows the RMS misfit between modelled

318 uplift and the cGPS observed uplift for all sites. When using all the cGPS data to constrain

319 the Earth models, the range of lithospheric thickness for the best fitting models narrows to

320 100–140 km and the acceptable range of upper mantle viscosity narrows to 6 × 1017 – 2 ×

321 1018 Pa s, as indicated by the 95% confidence limit. The Earth model with the lowest RMS

322 misfit (4.38 mm) has values of 120 km and 1 × 1018 Pa s.

13

323 The model-predicted time series for the best fitting Earth models in Figs. 3a and 3b are

324 plotted against the cGPS time series in Fig. 4. For comparison, predicted time series using the

325 “VM2” Earth model, the viscosity structure which accompanies the global ICE-5G GIA

326 model (Peltier 2004), are also plotted, along with time series calculated using an Earth model

327 within the ranges suggested by Ivins et al. (2011) (an incompressible model as used in (Ivins

328 et al., 2011) with 40 km lithosphere and 3 × 1019 Pa s upper mantle viscosity). There is little

329 difference between our two best fit models, whereas both VM2 and the Ivins et al. (2011)

330 models under-predict uplift at all cGPS locations. The uplift predicted by the VM2 and Ivins

331 models is dominated by the elastic part of the signal, and the viscous contribution is small.

332 For example, at FONP the viscous part of the total uplift at 2013.0 is 22 mm for the Ivins et

333 al. (2011) model, and only 1 mm for VM2, compared with 123-130 mm for our best fitting

334 models. In the supplementary material we compare the model-predicted uplift with GPS

335 records at two further locations: OHI2 and SPPT (see Fig. 1 for locations), and this is

336 discussed in Section 5.

337 The spatial distribution of model-predicted uplift rates (estimated over the same time

338 period as the cGPS observed uplift rate, i.e. 2009.0 – 2013.0) for the elastic and viscous

339 components are shown in Figs. 5a and 5b, respectively, the latter based on the best-fitting

340 Earth model from Fig. 3b, as constrained by all seven cGPS sites. Fig. 5c shows the sum of

341 panels a and b and represents the viscoelastic uplift rates including the uniform background

342 rate, with cGPS uplift rates over-plotted (as per Table 3). The observed cGPS uplift rates are

343 well reproduced by the model.

344

345 5. Discussion

346 5.1. Earth Model

14

347 Using the ice-mass change dataset and observations from seven cGPS stations we have

348 been able to constrain a range of Earth models for the NAP. We first used Palmer station only

349 to constrain the Earth model, as the background uplift rate due to long-term glacial isostatic

350 adjustment is well constrained by the pre-2002 data, available only at this site. The addition

351 of the six LARISSA cGPS sites narrows the overall range of best fitting Earth models to a

352 lithospheric thickness between 100 km and 140 km and upper mantle viscosity in the range

353 6 × 1017 – 2 × 1018 Pa s. Using a uniform background rate for the whole region may introduce

354 some error in these results if the signal is in fact spatially variable, as suggested by Nield et

355 al. (2012). Nonetheless, using the LARISSA cGPS data provides some verification for the

356 inferences from the Palmer dataset. To test the sensitivity to a spatially constant background

357 rate, we computed a new background rate based on that estimated from Palmer, but scaled at

358 the other cGPS locations according to the spatial pattern of the W12a Antarctic GIA model

359 (Whitehouse et al., 2012). Computing the RMS again for all cGPS sites does not change the

360 best fitting model and reduces the minimum RMS misfit by only 0.01 mm, giving further

361 confidence in our results. Furthermore, comparing the best fitting model-predicted uplift with

362 campaign GPS observations between 1997 and 2013 at the location of Spring Point, which

363 were not included as constraints on the model, shows a qualitatively good fit and strengthens

364 our conclusions (Fig. S3 in the supplementary material).

365 The Earth model with minimum RMS misfit in both cases (Figs. 3a and 3b) has a thick

366 lithosphere (120-130 km) and a low upper mantle viscosity (7 × 1017 – 1 × 1018 Pa s).

367 However, it is important to note that the solution is non-unique and within the 95%

368 confidence limit the RMS misfit varies by less than 1 mm, so any model within this limit can

369 provide a reasonable fit to the data. The combination of thick lithosphere and low upper

370 mantle viscosity is somewhat unexpected, as low viscosity regions are commonly

371 accompanied by a thinner lithosphere (e.g. Auriac et al., 2013; Lange et al., 2014; Simms et

15

372 al., 2012). However, as described in Section 4.2, computing the RMS misfit of Palmer using

373 only pre-2011 data gives a best fitting lithospheric thickness of 20 km, which highlights our

374 poor sensitivity to lithospheric thickness. Similarly, when discounting data before 1999.5

375 which may be affected by a possible offset in the Palmer time series, the best fitting

376 lithospheric thickness is reduced to 30 km. In contrast, we robustly determine an upper

377 mantle viscosity of less than 2 × 1018 Pa s (the upper limit of the 95% confidence interval) is

378 required to fit the available data. A low viscosity upper mantle is consistent with the back-arc

379 setting and evidence of recent volcanism in the region.

380 Our range of Earth models is different to those determined by Ivins et al. (2011) for a

381 larger region encompassing ours. Fig. 4 reveals that the Ivins et al. (2011) Earth model, when

382 combined with post-1995 ice unloading, cannot explain the rapid uplift at Palmer since 2002.

383 There are a number of possible reasons for this. First, Ivins et al. (2011) considered a single

384 Earth model for a region approximately three times larger than ours, and hence their model is

385 an average for this wider region. Second, the ice unloading scenarios considered by Ivins et

386 al. (2011) are based on relatively few observations and their Earth model may be

387 compensating for ice load errors in poorly constrained regions. Third, Ivins et al. (2011) were

388 limited in their ability to consider the non-linearity in the Palmer record, as their analysis

389 required them to combine it with the GRACE time series which started after 2002, and

390 therefore they treated it as a single linear rate over the post-2002 data period. Finally, it needs

391 to be verified if our Earth model could satisfactorily fit the observations of the kind used by

392 Ivins et al. (2011); if it cannot, then this may be an indication that use of higher-order

393 constitutive theories that exhibit non-linear creep response functions (see Ivins and Sammis

394 (1996), Figure 7 therein), and whose material parameters may be independently tested by

395 both laboratory and geophysical observation, must be considered.

16

396 The peak uplift predicted by our best fit Earth model is 47 mm/yr located in the

397 Hektoria/Green glacier basin (Fig. 5c), corresponding to the geographical location of the

398 largest mass loss (Berthier et al., 2012). The peak uplift is dominated by the elastic signal and

399 has a small spatial extent, diminishing to 30 mm/yr or less within ~30 km. Our nearest cGPS

400 site is located at Foyn Point (FONP), ~40 km away, where the observed uplift rate of 14.9 ±

401 2.7 mm/yr agrees well with the 16.4 mm/yr predicted by the model. Our rates may differ

402 from the true uplift for parts of the model domain if the long-term background uplift rate is

403 substantially different to the spatially constant term we have adopted; however, the closeness

404 of the fit between the LARISSA cGPS data and our model predictions suggests our first

405 approximation is reasonable.

406 5.2. Lateral Variations in Earth Structure

407 In using a 1-D symmetric Earth model we do not consider the effects of lateral

408 heterogeneity in Earth structure. As our study region is small, there are unlikely to be large

409 variations within the area covered by the cGPS stations. However, the long-term tectonic

410 history of the region suggests that there may be a gradient in Earth structure along the length

411 of the Peninsula (Barker 2001; Larter et al., 1997). This is supported by the recent study of

412 Simms et al. (2012) who predict a thinner lithosphere (15km) for the South Shetland Islands,

413 which lie 100 km off the northern tip of the AP. Due to the likely lateral variations in Earth

414 structure, we did not include any cGPS data far from the site of largest ice loss as constraints

415 (e.g. O’Higgins which lies 300 km to the north, OHI2 in Fig. 1), although we compare the

416 model-predicted uplift to these cGPS observations in Fig. S2 of the supplementary material.

417 Fig. S2 shows that the linear uplift recorded at O’Higgins cannot be explained by our model,

418 both in terms of the magnitude of uplift and linearity of the time series. This is likely due to a

419 combination of increased uncertainty in ice unloading near to O’Higgins over 1995-2001, the

420 different Earth structure and our assumption of a spatially constant background rate.

17

421 The Earth models inferred here show that the NAP cannot successfully be modelled as

422 part of a continent-wide GIA model, as the Earth structure is too different from that

423 traditionally used for the rest of Antarctica (e.g., Whitehouse et al., 2012). Our work has

424 important implications for forthcoming GIA models which incorporate 3-D Earth structure,

425 and it identifies a location where upper Earth structure may be constrained by observations.

426 5.3. Sensitivity to a Complex Earth Structure

427 We found that the cGPS observations can be explained reasonably well by a simple four-

428 layer viscous model, in which only the lithospheric thickness and upper mantle viscosity

429 parameters were varied. The depth over which the load induces mantle flow was tested by

430 decreasing the depth of the modelled upper mantle-transition zone boundary to 350 km. The

431 RMS of the two best fit models increased by 6-11% suggesting that mantle flow occurs to at

432 least this depth. Increasing or decreasing the transition zone viscosity by an order of

433 magnitude made less than 1% difference to the RMS for each best fit model. Our results are,

434 therefore, not sensitive to changes in Earth model parameters below 400 km depth due to the

435 small spatial extent of the load and observations. In view of this we consider the implications

436 of an Earth model with a more complex structure in the top 400 km.

437 Several studies that have used a more complex Earth structure include a low viscosity

438 zone (LVZ) directly beneath the elastic lithosphere (e.g., Sato et al., 2011). We performed

439 some sensitivity tests to investigate whether such a model could provide a better fit to the

440 data. Two thicknesses of the LVZ were tested (100 km and 200 km), along with several

441 different ratios of LVZ viscosity to upper mantle viscosity (1:5, 1:10, 1:20) (six experiments

442 in total). The results showed that whilst the single best fitting Earth model changed for each

443 experiment, the overall range within the 95% confidence limit remained broadly the same.

444 Furthermore, the minimum RMS misfit did not improve by more than 1%, demonstrating that

445 a significantly better fit to the data could not be achieved with a more complex Earth model.

18

446 A more spatially extensive cGPS network might in the future enable a more complex

447 Earth structure and lateral variations to be resolved and this network expansion is currently

448 underway as an extension of the LARISSA project, with a permanent site now installed at

449 Spring Point.

450 5.4. Sensitivity to Ice Model Uncertainties

451 As described in Section 2, we modelled ice-mass change over a longer time period than is

452 covered by the elevation change data by linearly extrapolating a constant rate of ice loss

453 backwards and forwards in time from a few months after ice shelf break up to the present

454 day, with no ramp up of mass change included. Studies have suggested that glaciers in the

455 NAP that have accelerated following an ice shelf collapse remain at elevated speeds for

456 decades. Rott et al. (2008) showed that Drygalski glacier, feeding the former Larsen A Ice

457 Shelf, did not accelerate between 1999 and 2007, and Rott et al. (2011) state that the

458 increased velocity of the Larsen A and Prince Gustav glaciers has so far been maintained 15

459 years after ice shelf collapse. The uncertainties in our ice model therefore relate to how

460 quickly Larsen B glaciers accelerated to reach the 2002-2006 rates (Fig. 1b), and the

461 acceleration history of Larsen A and Prince Gustav glaciers between 1995 and 1999.

462 To investigate this we simulated the acceleration of the glaciers in our ice loading model

463 by linearly increasing the rate of mass loss from 0 mweq/yr at the time of ice shelf collapse, to

464 full rates (as shown in Fig. 1) one year later for Larsen B and Larsen A/Prince Gustav

465 glaciers separately. For Larsen B glaciers this ramp up scenario of ice-mass loss improved the

466 RMS misfit by less than 5%, and similarly for Larsen A and Prince Gustav glaciers,

467 confirming that the effect of errors in our ice loading assumptions is small.

468 5.5. Elastic Effects of Surface Mass Balance Anomalies

469 Whilst the model output closely matches the cGPS time series overall, there are localised

470 misfits. This is likely due to local time variable mass changes which are not included in our

19

471 ice loading model. We investigated the possibility that these fluctuations are caused by an

472 elastic response to variations in surface mass balance (SMB) over shorter periods of time than

473 the DEMs allow us to resolve. SMB is dominated by iceberg calving, some melt runoff, and

474 accumulation.

475 Using the RACMO2.1/ANT27 dataset of SMB up to 2011.0 (Lenaerts et al., 2012), we

476 removed the long term trend to obtain anomalies to the mean at each grid point, and

477 converted them to a set of loading discs. The elastic response to the SMB anomalies was

478 calculated at Palmer, and superimposed onto the time series for the best fit viscoelastic model

479 from Fig. 3a. We perform this calculation with some caution due to the low resolution of the

480 SMB model (27km) compared with the small valley glaciers that dominate much of this

481 region (Trusel et al., 2013). Nevertheless, Fig. 6 shows that the additional elastic response

482 improves the fit between the modelled and observed time series and explains most of the

483 short-term variations, which likely reflect seasonal signals and multi-year perturbations in

484 SMB. The RMS misfit, calculated over the shorter time period of the SMB model, reduces

485 marginally from 4.74 mm to 4.56 mm. It is not known how the effect of SMB anomalies

486 could improve the fit at the other cGPS sites as the RACMO2.1/ANT27 model output is

487 presently only available up until the end of 2010, providing minimal overlap with the

488 LARISSA time series. A viscous response to SMB load changes is feasible but was not

489 considered, as due to the fluctuating nature of the SMB loads it is likely to be small.

490

491 6. Conclusions

492  Non-linear cGPS observed uplift from the NAP cannot be explained by the elastic

493 response of the Earth to ice-mass loss events relating to Larsen A, Prince Gustav, and

494 Larsen B ice shelf break-up.

20

495  A linear Maxwell viscoelastic model can produce a good fit to the Palmer cGPS

496 record, which constrains the upper mantle viscosity to less than 2 × 1018 Pa s, but the

497 lithospheric thickness remains poorly constrained.

498  Shorter time series from the six cGPS stations of the LARISSA network verify this

499 result, finding a best fitting Earth model with an upper mantle viscosity of 6 × 1017 –

500 2 × 1018 Pa s and narrowing the lithospheric thickness to 100–140 km, although the

501 analysis is limited by the assumption of a spatially uniform background rate.

502  A more complex Earth structure, in terms of vertical stratification, could explain the

503 observed data equally well, but additional cGPS stations are required to resolve this

504 structure further.

505  Reconciliation of present-day rates of bedrock uplift with average rates over longer

506 timescales may require rheological models that exhibit a non-linear response.

507  In regions of low upper mantle viscosity and on-going ice-mass change, cGPS data

508 cannot be correctly interpreted without considering the viscoelastic response to

509 present-day ice-mass change.

510

511 Acknowledgements: G.A.N. is supported by a NERC PhD studentship, M.A.K. is a recipient

512 of an Australian Research Council Future Fellowship (project number FT110100207), and

513 P.L.W. is a recipient of a NERC Independent Research Fellowship. VE-CL0V3RS was

514 developed by V.R.B and A.B in a self-funded project. Installation of the LARISSA cGPS

515 network was supported by NSF grant OPP-ANT-0732467 to EWD while data acquisition and

516 station vitality are supported by UNAVCO. Support of field logistics for station installation

517 was provided by the crew and staff aboard the USAP vessels L.M. Gould and N.B. Palmer;

518 we thank them and LARISSA colleagues for invaluable assistance. E.B. acknowledges

519 support from the French Space Agency (CNES) through the TOSCA and ISIS programs.

21

520 SPOT5 DEM were provided by the SPIRIT project (Korona et al., 2009) funded by the

521 French Space Agency (CNES). We acknowledge Christopher Shuman of the University of

522 Maryland, Baltimore County and Terry Haran of NSIDC for their contributions to the

523 elevation change data set. We also thank Michael Bevis for helpful discussions on the Palmer

524 time series, and Michiel van den Broeke and Jan Lenaerts for providing SMB output from

525 RACMO2.1/ANT27. Figures have been generated using the GMT software (Wessel and

526 Smith 1998). Erik Ivins and an anonymous reviewer are thanked for their comments that

527 helped clarify and improve the manuscript.

528

529 References

530

531 Agnew, D.C. 1996, SPOTL: Some programs for ocean-tide loading, Scripps Institution of

532 Oceanography, SIO Ref. Ser. 96-8, 35 pp.

533 Agnew, D.C. 1997, NLOADF: A program for computing ocean-tide loading, J. Geophys.

534 Res., 102(B3), 5109-5110, doi: 10.1029/96jb03458.

535 Altamimi, Z., Collilieux, X., Métivier, L. 2011, ITRF2008: an improved solution of the

536 international terrestrial reference frame, Journal of Geodesy, 85(8), 457-473, doi:

537 10.1007/s00190-011-0444-4.

538 Auriac, A., Spaans, K.H., Sigmundsson, F., Hooper, A., Schmidt, P., Lund, B. 2013, Iceland

539 rising: Solid Earth response to ice retreat inferred from satellite radar interferometry and

540 visocelastic modeling, Journal of Geophysical Research: Solid Earth, 118(4), 1331-1344, doi:

541 10.1002/jgrb.50082.

542 Barker, D.H.N., Austin, J.A. 1998, Rift propagation, detachment faulting, and associated

543 magmatism in Bransfield Strait, Antarctic Peninsula, Journal of Geophysical Research: Solid

544 Earth, 103(B10), 24017-24043, doi: 10.1029/98jb01117.

22

545 Barker, P.F. 1982, The Cenozoic subduction history of the Pacific margin of the Antarctic

546 Peninsula: ridge crest–trench interactions, Journal of the Geological Society, 139(6), 787-

547 801, doi: 10.1144/gsjgs.139.6.0787.

548 Barker, P.F. 2001, Scotia Sea regional tectonic evolution: implications for mantle flow and

549 palaeocirculation, Earth-Science Reviews, 55(1–2), 1-39, doi:

550 http://dx.doi.org/10.1016/S0012-8252(01)00055-1.

551 Barker, P.F., Dalziel, I.W.D., Storey, B.C., 1991, Tectonic Development of the Scotia Arc

552 Region, in: The Geology of Antarctica, (eds R.J. Tingey), Oxford University Press, pp. 215-

553 248.

554 Barletta, V.R., Ferrari, C., Diolaiuti, G., Carnielli, T., Sabadini, R., Smiraglia, C. 2006,

555 Glacier shrinkage and modeled uplift of the Alps, Geophys. Res. Lett., 33(14), L14307, doi:

556 10.1029/2006gl026490.

557 Berthier, E., Scambos, T.A., Shuman, C.A. 2012, Mass loss of Larsen B tributary glaciers

558 (Antarctic Peninsula) unabated since 2002, Geophys. Res. Lett., 39(13), L13501, doi:

559 10.1029/2012gl051755.

560 Bertiger, W., Desai, S., Haines, B., Harvey, N., Moore, A., Owen, S., Weiss, J. 2010, Single

561 receiver phase ambiguity resolution with GPS data, Journal of Geodesy, 84(5), 327-337, doi:

562 10.1007/s00190-010-0371-9.

563 Bevis, M., Kendrick, E., Smalley, R., Jr., Dalziel, I., Caccamise, D., Sasgen, I., Helsen, M.,

564 Taylor, F.W., Zhou, H., Brown, A., Raleigh, D., Willis, M., Wilson, T., Konfal, S. 2009,

565 Geodetic measurements of vertical crustal velocity in West Antarctica and the implications

566 for ice mass balance, Geochem. Geophys. Geosyst., 10(10), Q10005, doi:

567 10.1029/2009gc002642.

568 Boehm, J., Werl, B., Schuh, H. 2006, Troposphere mapping functions for GPS and very long

569 baseline interferometry from European Centre for Medium-Range Weather Forecasts

23

570 operational analysis data, Journal of Geophysical Research: Solid Earth, 111(B2), B02406,

571 doi: 10.1029/2005jb003629.

572 Cook, A.J., Vaughan, D.G. 2010, Overview of areal changes of the ice shelves on the

573 Antarctic Peninsula over the past 50 years, Cryosphere, 4(1), 77-98, doi: 10.5194/tc-4-77-

574 2010.

575 Cook, A.J., Fox, A.J., Vaughan, D.G., Ferrigno, J.G. 2005, Retreating Glacier Fronts on the

576 Antarctic Peninsula over the Past Half-Century, Science, 308(5721), 541-544, doi:

577 10.1126/science.1104235.

578 De Angelis, H., Skvarca, P. 2003, Glacier Surge After Ice Shelf Collapse, Science,

579 299(5612), 1560-1562, doi: 10.1126/science.1077987.

580 Dziewonski, A.M., Anderson, D.L. 1981, Preliminary reference Earth model, Physics of the

581 Earth and Planetary Interiors, 25(4), 297-356, doi: 10.1016/0031-9201(81)90046-7.

582 Egbert, G.D., Erofeeva, S.Y., Han, S.C., Luthcke, S.B., Ray, R.D. 2009, Assimilation of

583 GRACE tide solutions into a numerical hydrodynamic inverse model, Geophysical Research

584 Letters, 36(20), L20609, doi: 10.1029/2009gl040376.

585 Fu, Y., Freymueller, J., Dam, T. 2012, The effect of using inconsistent ocean tidal loading

586 models on GPS coordinate solutions, Journal of Geodesy, 86(6), 409-421, doi:

587 10.1007/s00190-011-0528-1.

588 González-Ferrán, O., 1983, The Larsen Rift: an active extension fracture in West Antarctica.,

589 in: Antarctic Earth Science, (eds R. Oliver, P. James, J. Jago), Cambridge University Press,

590 Melbourne, pp. 344-346.

591 Ivins, E.R., Sammis, C.G. 1996, Transient creep of a composite lower crust: 1. Constitutive

592 theory, Journal of Geophysical Research: Solid Earth, 101(B12), 27981-28004, doi:

593 10.1029/96jb02847.

24

594 Ivins, E.R., Watkins, M.M., Yuan, D.-N., Dietrich, R., Casassa, G., Rülke, A. 2011, On-land

595 ice loss and glacial isostatic adjustment at the Drake Passage: 2003-2009, J. Geophys. Res.,

596 116(B2), B02403, doi: 10.1029/2010jb007607.

597 King, M.A., Padman, L., Nicholls, K., Clarke, P.J., Gudmundsson, G.H., Kulessa, B.,

598 Shepherd, A. 2011, Ocean tides in the Weddell Sea: New observations on the Filchner-Ronne

599 and Larsen C ice shelves and model validation, Journal of Geophysical Research: Oceans,

600 116(C6), C06006, doi: 10.1029/2011jc006949.

601 Korona, J., Berthier, E., Bernard, M., Rémy, F., Thouvenot, E. 2009, SPIRIT. SPOT 5

602 stereoscopic survey of Polar Ice: Reference Images and Topographies during the fourth

603 International Polar Year (2007–2009), ISPRS Journal of Photogrammetry and Remote

604 Sensing, 64(2), 204-212, doi: http://dx.doi.org/10.1016/j.isprsjprs.2008.10.005.

605 Kunz, M., King, M.A., Mills, J.P., Miller, P.E., Fox, A.J., Vaughan, D.G., Marsh, S.H. 2012,

606 Multi-decadal glacier surface lowering in the Antarctic Peninsula, Geophys. Res. Lett.,

607 39(19), L19502, doi: 10.1029/2012gl052823.

608 Lange, H., Casassa, G., Ivins, E.R., Schröder, L., Fritsche, M., Richter, A., Groh, A.,

609 Dietrich, R. 2014, Observed crustal uplift near the Southern Patagonian Icefield constrains

610 improved viscoelastic Earth Models, Geophysical Research Letters, 2013GL058419, doi:

611 10.1002/2013gl058419.

612 LARsen Ice Shelf System, Antarctica (LARISSA), Updated 2013, Accessed 28 Aug 2013,

613 http://www.hamilton.edu/expeditions/larissa

614 Larter, R.D., Barker, P.F. 1991, Effects of ridge crest-trench interaction on Antarctic-Phoenix

615 Spreading: Forces on a young subducting plate, Journal of Geophysical Research: Solid

616 Earth, 96(B12), 19583-19607, doi: 10.1029/91jb02053.

617 Larter, R.D., Rebesco, M., Vanneste, L.E., GambôA, L.A.P., Barker, P.F., 1997, Cenozoic

618 Tectonic, Sedimentary and Glacial History of the Continental Shelf West Of ,

25

619 Antarctic Peninsula, in: Geology and Seismic Stratigraphy of the Antarctic Margin, 2, (eds

620 P.F. Barker, A.K. Cooper), American Geophysical Union, Washington, D. C, pp. 1-27.

621 Lenaerts, J.T.M., van den Broeke, M.R., van de Berg, W.J., van Meijgaard, E., Kuipers

622 Munneke, P. 2012, A new, high-resolution surface mass balance map of Antarctica (1979-

623 2010) based on regional atmospheric climate modeling, Geophys. Res. Lett., 39(4), L04501,

624 doi: 10.1029/2011gl050713.

625 Nield, G.A., Whitehouse, P.L., King, M.A., Clarke, P.J., Bentley, M.J. 2012, Increased ice

626 loading in the Antarctic Peninsula since the 1850s and its effect on glacial isostatic

627 adjustment, Geophys. Res. Lett., 39(17), L17504, doi: 10.1029/2012gl052559.

628 Peltier, W.R. 2004, Global Glacial Isostasy and the Surface of the Ice-Age Earth: The ICE-

629 5G (VM2) Model and GRACE, Annual Review of Earth and Planetary Sciences, 32(1), 111-

630 149, doi: doi:10.1146/annurev.earth.32.082503.144359.

631 Petit, G., Luzum, B. 2010, IERS Conventions. IERS Technical Note 36, Frankfurt am Main:

632 Verlag des Bundesamts für Kartographie und Geodäsie, 2010., 179.

633 Petrie, E., Hernández-Pajares, M., Spalla, P., Moore, P., King, M. 2011, A Review of Higher

634 Order Ionospheric Refraction Effects on Dual Frequency GPS, Surveys in Geophysics, 32(3),

635 197-253, doi: 10.1007/s10712-010-9105-z.

636 Pritchard, H.D., Vaughan, D.G. 2007, Widespread acceleration of tidewater glaciers on the

637 Antarctic Peninsula, J. Geophys. Res., 112(F3), F03S29, doi: 10.1029/2006jf000597.

638 Rack, W., Rott, H. 2004, Pattern of retreat and disintegration of the Larsen B ice shelf,

639 Antarctic Peninsula, Annals of Glaciology, 39, 505-510, doi: 10.3189/172756404781814005.

640 Rignot, E., Casassa, G., Gogineni, P., Krabill, W., Rivera, A., Thomas, R. 2004, Accelerated

641 ice discharge from the Antarctic Peninsula following the collapse of Larsen B ice shelf,

642 Geophys. Res. Lett., 31(18), L18401, doi: 10.1029/2004gl020697.

26

643 Rott, H., Skvarca, P., Nagler, T. 1996, Rapid Collapse of Northern Larsen Ice Shelf,

644 Antarctica, Science, 271(5250), 788-792, doi: 10.1126/science.271.5250.788.

645 Rott, H., Eineder, M., Nagler, T., Floricioiu, D. 2008, New Results on Dynamic Instability of

646 Antarctic Peninsula Glaciers detected by TerraSAR-X Ice Motion Analysis, Proceedings of

647 7th European Conference on Synthetic Aperture Radar (EUSAR), VDE Verlag, Berlin,

648 Germany, 159-162.

649 Rott, H., Müller, F., Nagler, T., Floricioiu, D. 2011, The imbalance of glaciers after

650 disintegration of Larsen-B ice shelf, Antarctic Peninsula, The Cryosphere, 5(1), 125-134, doi:

651 10.5194/tc-5-125-2011.

652 Sato, T., Larsen, C.F., Miura, S., Ohta, Y., Fujimoto, H., Sun, W., Motyka, R.J., Freymueller,

653 J.T. 2011, Reevaluation of the viscoelastic and elastic responses to the past and present-day

654 ice changes in Southeast Alaska, Tectonophysics, 511(3–4), 79-88, doi:

655 10.1016/j.tecto.2010.05.009.

656 Scambos, T.A., Bohlander, J.A., Shuman, C.A., Skvarca, P. 2004, Glacier acceleration and

657 thinning after ice shelf collapse in the Larsen B embayment, Antarctica, Geophys. Res. Lett.,

658 31(18), L18402, doi: 10.1029/2004gl020670.

659 Scambos, T.A., Berthier, E., Haran, T., Shuman, C., Cook, A., Ligtenberg, S., Bohlander, J.

660 2014, Quantifying patterns of mass loss in the northern Antarctic Peninsula, Nature

661 Geoscience, in review.

662 Shuman, C.A., Berthier, E., Scambos, T.A. 2011, 2001-2009 elevation and mass losses in the

663 Larsen A and B embayments, Antarctic Peninsula, Journal of Glaciology, 57(204), 737-754,

664 doi: 10.3189/002214311797409811.

665 Simms, A.R., Ivins, E.R., DeWitt, R., Kouremenos, P., Simkins, L.M. 2012, Timing of the

666 most recent Neoglacial advance and retreat in the South Shetland Islands, Antarctic

27

667 Peninsula: insights from raised beaches and Holocene uplift rates, Quaternary Science

668 Reviews, 47(0), 41-55, doi: 10.1016/j.quascirev.2012.05.013.

669 Spada, G., Barletta, V.R., Klemann, V., Riva, R.E.M., Martinec, Z., Gasperini, P., Lund, B.,

670 Wolf, D., Vermeersen, L.L.A., King, M.A. 2011, A benchmark study for glacial isostatic

671 adjustment codes, Geophysical Journal International, 185(1), 106-132, doi: 10.1111/j.1365-

672 246X.2011.04952.x.

673 Thomas, I.D., King, M.A., Bentley, M.J., Whitehouse, P.L., Penna, N.T., Williams, S.D.P.,

674 Riva, R.E.M., Lavallee, D.A., Clarke, P.J., King, E.C., Hindmarsh, R.C.A., Koivula, H. 2011,

675 Widespread low rates of Antarctic glacial isostatic adjustment revealed by GPS observations,

676 Geophys. Res. Lett., 38(22), L22302, doi: 10.1029/2011gl049277.

677 Trusel, L.D., Frey, K.E., Das, S.B., Munneke, P.K., van den Broeke, M.R. 2013, Satellite-

678 based estimates of Antarctic surface meltwater fluxes, Geophysical Research Letters, 40(23),

679 2013GL058138, doi: 10.1002/2013GL058138.

680 van Dam, T. 2010, Updated October 2010. NCEP Derived 6-hourly, global surface

681 displacements at 2.5 x 2.5 degree spacing. Data set accessed 2013-01-16 at

682 http://geophy.uni.lu/ncep-loading.html.

683 Wendt, J., Rivera, A., Wendt, A., Bown, F., Zamora, R., Casassa, G., Bravo, C. 2010, Recent

684 ice-surface-elevation changes of Fleming Glacier in response to the removal of the Wordie

685 Ice Shelf, Antarctic Peninsula, Annals of Glaciology, 51(55), 97-102, doi:

686 10.3189/172756410791392727.

687 Wessel, P., Smith, W.H.F. 1998, New, improved version of generic mapping tools released,

688 Eos, Transactions American Geophysical Union, 79(47), 579-579, doi: 10.1029/98eo00426.

689 Whitehouse, P.L., Bentley, M.J., Milne, G.A., King, M.A., Thomas, I.D. 2012, A new glacial

690 isostatic adjustment model for Antarctica: calibrated and tested using observations of relative

28

691 sea-level change and present-day uplift rates, Geophysical Journal International, doi:

692 10.1111/j.1365-246X.2012.05557.x.

693 Williams, S. 2008, CATS: GPS coordinate time series analysis software, GPS Solutions,

694 12(2), 147-153, doi: 10.1007/s10291-007-0086-4.

695 Zumberge, J.F., Heflin, M.B., Jefferson, D.C., Watkins, M.M., Webb, F.H. 1997, Precise

696 point positioning for the efficient and robust analysis of GPS data from large networks,

697 Journal of Geophysical Research: Solid Earth, 102(B3), 5005-5017, doi: 10.1029/96jb03860.

698

699

700

29

701 Figures

702

703 Fig. 1. Observed ice-mass change rate given in metres water equivalent per year. a) The full

704 study area with cGPS locations shown as pink circles and former ice shelf locations as dashed

705 black lines (Prince Gustav (PG), Larsen A (LA) and Larsen B (LB)). Values in the Larsen B

706 area (see Fig. 1b) represent the mean rate of change for the period 2001-2006, values

707 elsewhere represent the mean rate of change for the period 2003-2009. Inset shows location

708 of the study area. b) Ice-mass change for Larsen B only using 2001-2006 data. c) Ice-mass

709 change for Larsen B only using 2006-2011 data. H-G is the Hektoria-Green drainage basin.

710

30

711 Fig. 2. Palmer cGPS observations (grey dots) compared with uplift time series predicted by

712 the elastic model (red line). Predicted elastic uplift time series for upper and lower bounds on

713 ice-mass loss is shown by the orange dashed lines; and predicted uplift time series assuming

714 5 times the observed ice-mass loss is shown by the green line with squares.

715

716

31

717 Fig. 3. RMS misfit between modelled viscoelastic uplift time series and cGPS observed time

718 series for a) Palmer only, and b) Palmer and all stations of the LARISSA network. The 95%

719 confidence limit is plotted as a solid black line, and the best fit Earth model in each case is

720 plotted as a red star.

721

722

32

723 Fig. 4. cGPS observations (grey dots) and model-predicted uplift time series at each cGPS

724 location for: the best fitting viscoelastic Earth model in Fig. 3a (red line), the best fitting

725 viscoelastic Earth model in Fig. 3b (blue squares), the Ivins et al. (2011) viscoelastic Earth

726 model (orange line), and the VM2 viscoelastic Earth model (green dashed line). Map shows

727 cGPS locations.

728

33

729 Fig. 5. Uplift rates at 2011 for the best fitting viscoelastic Earth model in Fig. 3b; (a) elastic

730 only, (b) viscous only, and (c) combined viscoelastic and background rate. Post-2009 cGPS

731 uplift rates are plotted as circles using the same colour scale.

732

733 Fig. 6. Palmer cGPS observations (grey dots) and model-predicted uplift time series for the

734 best fitting Earth model in Fig. 3a (red line), and the best fitting Earth model with the

735 addition of the elastic effects of SMB anomalies (pale blue line).

736

34

737 Tables

738

739 Table 1: Location of cGPS stations, observing period, and observed uplift velocities.

Site Latitude (°) Longitude (°) Observing Period cGPS Observed Uplift (mm/yr) Palmer -64.78 -64.05 1998.5 – 2013.0 6.6 ± 2.1 (PALM) (2009.0‒2013.0 only) Cape Framnes -66.01 -60.56 2010.1 – 2013.0 (CAPF) 4.5 ± 2.9 Duthier’s -64.81 -62.82 2009.3 – 2013.0 Point (DUPT) 12.8 ± 2.1 Foyn Point -65.25 -61.65 2010.1 – 2013.0 (FONP) 14.9 ± 2.7 Hugo Island -64.96 -65.67 2009.3 – 2013.0 (HUGO) 1.7 ± 3.3 Robertson -65.25 -59.44 2010.1 – 2013.0 Island (ROBI) 7.8 ± 2.9 Vernadsky -65.25 -64.25 2010.1 – 2013.0 (VNAD) 5.8 ± 2.4 740

741 Table 2: Earth model parameters, with those that have been varied underlined.

Depth to base (km) Viscosity (Pa s)

Lithosphere 20 – 160 km 1 x 1051

Upper Mantle 400 1 x 1017 – 1 x 1020

Transition Zone 670 4 x 1020

Lower Mantle - 1 x 1022 742

743

35

744 Table 3: cGPS observed uplift velocities with 2-sigma error; model-predicted uplift

745 velocities for the elastic only model and the best fitting viscoelastic model from Fig. 3a. Both

746 model-predicted uplift velocities include the estimated background rate. Last column shows

747 the residual between observed and modelled viscoelastic uplift.

Residual (cGPS cGPS Observed Uplift Elastic Modelled Viscoelastic Modelled Site minus viscoelastic (mm/yr) Uplift (mm/yr) Uplift (mm/yr) model) (mm/yr) 6.6 ± 2.1 PALM 1.5 7.9 -1.3 (2009.0‒2013.0 only) CAPF 4.5 ± 2.9 0.4 7.3 -2.8

DUPT 12.8 ± 2.1 1.7 10.4 2.4

FONP 14.9 ± 2.7 6.7 16.4 -1.5

HUGO 1.7 ± 3.3 -0.4 2.8 -1.1

ROBI 7.8 ± 2.9 1.0 9.8 -2.0

VNAD 5.8 ± 2.4 0.01 5.9 -0.1 748

749

750

36

751 Supplementary Material

752 Fig. S1. Bathymetry of the study region showing the location of the active subduction zone

753 (South Shetland Trench), the Bransfield Basin and the Passive Margin. cGPS locations are

754 shown in red. Bathymetry data is taken from Arndt et al. (2013).

755 Arndt, J.E., Schenke, H.W., Jakobsson, M., Nitsche, F.O., Buys, G., Goleby, B., Rebesco,

756 M., Bohoyo, F., Hong, J., Black, J., Greku, R., Udintsev, G., Barrios, F., Reynoso-Peralta,

757 W., Taisei, M., Wigley, R. 2013, The International Bathymetric Chart of the Southern Ocean

758 (IBCSO) Version 1.0—A new bathymetric compilation covering circum-Antarctic waters,

759 Geophysical Research Letters, 40(12), 3111-3117, doi: 10.1002/grl.50413.

760

37

761 Fig. S2. cGPS observations (dots) and model-predicted uplift time series at O’Higgins for the

762 best fitting viscoelastic Earth model in Fig. 3a (red line) and the best fitting viscoelastic Earth

763 model in Fig. 3b (blue squares). The model-predicted uplift includes the background rate

764 derived from Palmer. The O’Higgins cGPS time series is made up of OHIG (dark grey dots),

765 and its replacement antenna OHI2 (light grey dots). OHI3, from the adjacent station, is also

766 shown (offset) in the orange dots. Note that the O’Higgins time series was not used to

767 constrain the Earth model.

768

769

38

770 Fig. S3. Campaign GPS observations (grey dots) with error bars and model-predicted uplift

771 time series at Spring Point (SPPT) for the best fitting viscoelastic Earth model in Fig. 3a (red

772 line) and the best fitting viscoelastic Earth model in Fig. 3b (blue squares). The model-

773 predicted uplift includes the background rate derived from Palmer. Note that the Spring Point

774 time series was not used to constrain the Earth model.

775

39